Video Transcript
Given that 𝐴 is equal to three, negative three, negative five and 𝐵 is equal to
three, five, two, what is the matrix 𝐴 minus the transpose of 𝐵?
The first thing we notice about this question is that 𝐴 is a one-by-three matrix,
and 𝐵 is a three-by-one matrix. When performing matrix addition and subtraction, we require the two matrices to be of
the same order. Currently, 𝐴 and 𝐵 are not of the same order. However, we’ve not been asked to perform a calculation using these two matrices. As we can see, we’ve been asked to find 𝐴 minus the transpose of 𝐵. So let’s start by finding the transpose of 𝐵.
When finding the transpose of a matrix, we take the rows of the original matrix and
turn them into the columns of the transpose matrix. So the first column of the transpose of 𝐵 will be the first row of 𝐵, which is just
three. The second column will be the second row, so that’s five. And the third column will be the third row, which is two. So we found that the transpose of 𝐵 is equal to three, five, two. However, now, instead of being a three-by-one matrix, it’s now a one-by-three matrix,
which we can see matches the order of 𝐴.
So now, we are able to carry out the calculation 𝐴 minus the transpose of 𝐵. When performing this calculation, we simply need to subtract each of the elements of
the transpose of 𝐵 from their corresponding elements of 𝐴. Since the first element of 𝐴 is three and the first element of the transpose of 𝐵
is also three, the first element of 𝐴 minus the transpose of 𝐵 will be three minus
three. The second element will be negative three minus five, and the third element will be
negative five minus two. Now, what we need to do is simplify these elements and we’ll reach our solution. We have that 𝐴 minus the transpose of 𝐵 is equal to the one-by-three matrix zero,
negative eight, negative seven.
